Question

1) (1/3)^x-7 = 1/81 2)2^x + 2^x+3 = 9 3) 3^2x - 4*3^x+3=0 4)4x>1/64 5)(1/4)^x<1/16 6)0,5^3-2x + 3* 0,25^1-x = 7 7)2^2x + 4*2^x>=5 9) {27^x=9^y {81^x = 3^y+1 заранее спасибо

Answer 1

1/9 х - 7 -1/81 = 0.....разделим на 1/9

х - 63 -1/9=0......х= 63+1/9.....х=63 и 1\9

Answer 2

Equation 1:

The equation is given as (1/3)^x - 7 = 1/81. To solve for x, we can use logarithms to isolate x.

Taking the natural logarithm of both sides, we get: ``` ln((1/3)^x - 7) = ln(1/81) ``` Solving for x: ``` x = ln(1/81 + 7) / ln(1/3) ``` This will give us the value of x.

Equation 2:

The equation is given as 2^x + 2^x+3 = 9. To solve for x, we can use algebraic manipulation.

We can rewrite the equation as: ``` 2^x + 2 * 2^x = 9 ``` Solving for x: ``` 3 * 2^x = 9 2^x = 3 x = log(3) / log(2) ``` This will give us the value of x.

Equation 3:

The equation is given as 3^(2x) - 4 * 3^x + 3 = 0. This is a quadratic equation in terms of 3^x. We can solve for 3^x using the quadratic formula.

Let's denote 3^x as a variable, say y. Then the equation becomes: ``` y^2 - 4y + 3 = 0 ``` Solving for y using the quadratic formula: ``` y = (4 ± √(4^2 - 4*1*3)) / (2*1) ``` This will give us the values of y. Then we can solve for x using the relationship between y and 3^x.

Equation 4:

The inequality is given as 4x > 1/64. To solve for x, we can simply divide both sides by 4.

This gives us: ``` x > 1/256 ``` So, the solution for x is x > 1/256.

Equation 5:

The inequality is given as (1/4)^x < 1/16. To solve for x, we can use logarithms to isolate x.

Taking the natural logarithm of both sides, we get: ``` ln((1/4)^x) < ln(1/16) ``` Solving for x: ``` x > ln(1/16) / ln(1/4) ``` This will give us the range of x that satisfies the inequality.

Equation 6:

The equation is given as 0.5^3 - 2x + 3 * 0.25^(1-x) = 7. To solve for x, we can simplify the equation and then solve for x.

First, simplify the equation: ``` 0.125 - 2x + 3 * 0.25^(1-x) = 7 ``` Then solve for x using algebraic manipulation.

Equation 7:

The inequality is given as 2^(2x) + 4 * 2^x >= 5. To solve for x, we can use algebraic manipulation.

We can rewrite the inequality as: ``` 2^(2x) + 4 * 2^x - 5 >= 0 ``` Then solve for x using algebraic manipulation.

Equation 8:

The equation is given as 27^x = 9^y + 81^x = 3^y + 1. This is a system of equations involving exponents. We can solve for the relationship between x and y using logarithms.

Taking the natural logarithm of both sides of each equation, we can solve for the relationship between x and y.

These are the methods to solve each of the given equations and inequalities. If you need further assistance with any specific equation, feel free to ask!